Best Known (150, ∞, s)-Nets in Base 3
(150, ∞, 81)-Net over F3 — Constructive and digital
Digital (150, m, 81)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (150, 80)-sequence over F3, using
- t-expansion [i] based on digital (144, 80)-sequence over F3, using
- base reduction for sequences [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- base reduction for sequences [i] based on digital (32, 80)-sequence over F9, using
- t-expansion [i] based on digital (144, 80)-sequence over F3, using
(150, ∞, 120)-Net over F3 — Digital
Digital (150, m, 120)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (150, 119)-sequence over F3, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 113 and N(F) ≥ 120, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
(150, ∞, 314)-Net in Base 3 — Upper bound on s
There is no (150, m, 315)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (150, 1568, 315)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31568, 315, S3, 5, 1418), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 8 302693 398416 304672 094817 663445 290480 699023 974489 861152 004499 047185 317977 824576 200902 215559 371924 321443 327666 031823 502849 329237 099864 847370 463061 995430 533438 341919 216957 822305 931613 909628 049040 354390 568570 945147 702829 177093 994833 692031 079597 601797 904574 946771 460898 255763 577368 467405 459082 193030 051639 158044 237193 811603 548824 145801 344495 526793 166933 686344 340909 387703 945387 647333 974265 104513 493477 160339 452282 081151 223876 456045 008168 372567 623691 934000 366215 991047 474090 566160 144816 028039 467588 145811 550186 244436 379505 655835 482434 852563 068433 406542 090641 259404 716551 063317 287718 691238 990932 997843 828161 974469 231737 706783 859692 405595 766886 189074 060573 596331 097042 497922 613317 924520 504947 014152 369215 317244 365296 074214 532802 893525 770390 740465 672604 153581 / 473 > 31568 [i]
- extracting embedded OOA [i] would yield OOA(31568, 315, S3, 5, 1418), but